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          单级放大器
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        <p>单级放大器可以分为四种基本类型：</p>
<ul>
<li>共源结构；</li>
<li>共栅结构；</li>
<li>源级跟随器；</li>
<li>共源共栅结构；</li>
</ul>
<a id="more"></a>
<h1 id="电阻负载的共源级">1. 电阻负载的共源级</h1>
<p>借助 MOS 管的跨导，可以将栅源电压转化为小信号漏极电流，再通过电阻将电流转为电压。</p>
<center>
<img style="zoom:67%; border-radius: 0.3125em; margin: auto;" src="https://pic.zhouyuqian.com/img/20210727194850.svg"> <br>
<div style="color:orange; border-bottom: 1px solid #d9d9d9;
    display: inline-block;
    color: #999;
    padding: 2px;">
图1.1 采用电阻负载的共源极
</div>
</center>
<p>图1.1(a)是一个采用电阻负载的共源极放大器，首先分析其大信号特性：</p>
<p>如果输入电压从零开始增大，则 M1 工作状态会有这样的变化：截止区 -&gt; 饱和区 -&gt; 线性区。</p>
<p>当 <span class="math inline">\(V_{in} &lt; V_{TH} 时，\)</span> M1 工作在截止区： <span class="math display">\[
V_{out} = V_{DD}
\]</span> 当 <span class="math inline">\(V_{in}\)</span> 接近 <span class="math inline">\(V_{TH}\)</span> 时，M1 开始导通，电流流过 <span class="math inline">\(R_D\)</span>，使 <span class="math inline">\(V_{out}\)</span> 减小，如果 <span class="math inline">\(V_{DD}\)</span> 不是特别小，则 M1 饱和导通： <span class="math display">\[
V_{out} = V_{DD} - R_D \frac{1}{2} \mu _n C_{ox} \frac{W}{L} (V_{in} - V_{TH}) ^2
\]</span> 当 <span class="math inline">\(V_{in}\)</span> 继续增大，<span class="math inline">\(V_{out}\)</span> 继续下降，直到 <span class="math inline">\(V_{out} = V_{in} - V_{TH}\)</span> 时，M1 到达饱和区与线性区的临界状态： <span class="math display">\[
V_{in1} - V_{TH} = V_{out} = V_{DD} - R_D \frac{1}{2} \mu _n C_{ox} \frac{W}{L} (V_{in1} - V_{TH}) ^2
\]</span> 当 <span class="math inline">\(V_{in} &gt; V_{in1}\)</span> 时，M1 工作在线性区： <span class="math display">\[
V_{out}= V_{DD} - R_D \frac{1}{2} \mu _n C_{ox} \frac{W}{L} [ 2(V_{in1} - V_{TH}) V_{out} - V_{out} ^2 ]
\]</span> 当 <span class="math inline">\(V_{in}\)</span> 继续增大，<span class="math inline">\(V_{out} &lt;&lt; 2(V_{in} - V_{TH})\)</span> 时，M1 工作在深线性区，等效电路如图1.1(c)所示： <span class="math display">\[
V_{out} = V_{DD} \frac{R_{on}}{R_{on} + R_D} = \frac{V_{DD}}{1+\mu _n C_{ox} \frac{W}{L} R_D (V_{in} - V_{TH})}
\]</span> 因此其输入输出特性曲线如图1.2所示。</p>
<center>
<img style="zoom:133%; border-radius: 0.3125em; margin: auto;" src="https://pic.zhouyuqian.com/img/20210727194906.svg"> <br>
<div style="color:orange; border-bottom: 1px solid #d9d9d9;
    display: inline-block;
    color: #999;
    padding: 2px;">
图1.2 采用电阻负载的共源极
</div>
</center>
<p>分析其小信号特性，当 <span class="math inline">\(V_{out} &gt; V_{in} - V_{TH}\)</span> 时，即在图1.2 A 点左侧时，曲线的斜率可以看做小信号增益： <span class="math display">\[
\begin{split}
A_v = {}&amp; \frac{\partial V_{out}}{\partial V_{in}} \\
= {}&amp; - R_D \mu _n C_{ox} \frac{W}{L} (V_{in} - V_{TH}) \\
= {}&amp; -g_m R_D
\end{split}
\]</span> 由于 <span class="math inline">\(g_m\)</span> 会随输入 <span class="math inline">\(V_{in}\)</span> 变化，因此在大信号时，增益会发生较大的变化，该结构的增益线性度不好。</p>
<h1 id="二极管负载的共源极">2. 二极管负载的共源极</h1>
<h2 id="电路分析">电路分析</h2>
<p>如图2.1(a)所示，将 MOS 管的删漏短接，该 MOS 管可以起一个小信号电阻的作用。</p>
<center>
<img style="zoom:67%; border-radius: 0.3125em; margin: auto;" src="https://pic.zhouyuqian.com/img/20210727194925.svg"> <br>
<div style="color:orange; border-bottom: 1px solid #d9d9d9;
    display: inline-block;
    color: #999;
    padding: 2px;">
图2.1 Diode MOS
</div>
</center>
<p>由于 <span class="math inline">\(V_G = V_D\)</span>，因此该 MOS 管工作在饱和区，图2.1(b)为小信号等效电路，<span class="math inline">\(V_1 = V_X\)</span>，<span class="math inline">\(I_X = V_X/r_o + g_m V_X\)</span>，所以二极管的阻抗等于： <span class="math display">\[
r_{equ} = (1/g_m) || r_o \approx 1/g_m
\]</span> 如果存在体效应，则如图2.1(c)和图2.1(d)的小信号等效电路，<span class="math inline">\(V_1 = -V_X\)</span>，<span class="math inline">\(V_{bs} = -V_X\)</span>，则： <span class="math display">\[
(g_m + g_{mb})V_X + \frac{V_X}{r_o} = I_X
\]</span> —&gt; <span class="math display">\[
r_{eq} = \frac{V_X}{I_X} = \frac{1}{g_m+g_{mb}} || r_o \approx \frac{1}{g_m+g_{mb}}
\]</span></p>
<center>
<img style="zoom:67%; border-radius: 0.3125em; margin: auto;" src="https://pic.zhouyuqian.com/img/20210727194943.svg"> <br>
<div style="color:orange; border-bottom: 1px solid #d9d9d9;
    display: inline-block;
    color: #999;
    padding: 2px;">
图2.2 采用二极管负载的共源极
</div>
</center>
<p>分析二极管负载的共源极，如图2.2所示，忽略沟道长度调制效应，则： <span class="math display">\[
\begin{split}
A_v = {}&amp; -g_{m1}\frac{1}{g_{m2}+g_{mb}} \\
={}&amp; -\frac{g_{m1}}{g_{m2}} \frac{1}{1+\eta} \\
\\
\eta = {}&amp; \frac{g_{mb2}}{g_{m2}}
\end{split}
\]</span></p>
<p><span class="math display">\[
A_v = -\frac{\sqrt{2\mu _n C_{ox} (W/L)_1 I_{D1}}}{\sqrt{2\mu _n C_{ox} (W/L)_2 I_{D2}}} \frac{1}{1+\eta}
\]</span></p>
<p>因为 <span class="math inline">\(I_{D1} = I_{D2}\)</span>，则： <span class="math display">\[
A_v = -\frac{\sqrt{(W/L)_1}}{\sqrt{(W/L)_2}} \frac{1}{1+\eta}
\]</span> 由等式可以看出，如果忽略 <span class="math inline">\(1/{1+\eta}\)</span> 随输出电压的变化，则只要 MOS 管工作在饱和区，增益和偏置电压电流没有关系。这表明输入输出特性呈线性。</p>
<h2 id="仿真">仿真</h2>
<center>
<img style="zoom:100%; border-radius: 0.3125em; margin: auto;" src="https://pic.zhouyuqian.com/img/20210727195002.png"> <br>
<div style="color:orange; border-bottom: 1px solid #d9d9d9;
    display: inline-block;
    color: #999;
    padding: 2px;">
图2.3 二极管负载的共源极schematic
</div>
</center>
<ul>
<li>DC</li>
</ul>
<table>
<thead>
<tr class="header">
<th>器件</th>
<th>参数</th>
<th>值</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>M0</td>
<td>L</td>
<td>1u</td>
</tr>
<tr class="even">
<td>M0</td>
<td>W</td>
<td>10u</td>
</tr>
<tr class="odd">
<td>M1</td>
<td>L</td>
<td>1u</td>
</tr>
<tr class="even">
<td>M2</td>
<td>W</td>
<td>10u</td>
</tr>
</tbody>
</table>
<center>
<img style="zoom:100%; border-radius: 0.3125em; margin: auto;" src="https://pic.zhouyuqian.com/img/20210727195016.jpg"> <br>
<div style="color:orange; border-bottom: 1px solid #d9d9d9;
      display: inline-block;
      color: #999;
      padding: 2px;">
图2.6 DC
</div>
</center>
<ul>
<li><p>M0 L sweep</p>
<p>M1 参数不变，M0 W 不变，L 从 0.1u - 10u</p>
<center>
<p><img style="zoom:100%; border-radius: 0.3125em; margin: auto;" src="https://pic.zhouyuqian.com/img/20210727195029.jpg"> <br></p>
<div style="color:orange; border-bottom: 1px solid #d9d9d9;
    display: inline-block;
    color: #999;
    padding: 2px;">
图2.7 L0 sweep
</div>
</center></li>
<li><p>M0 W sweep</p>
<p>M1 参数不变，M0 L 不变，W 从 1u - 100u</p>
<center>
<p><img style="zoom:100%; border-radius: 0.3125em; margin: auto;" src="https://pic.zhouyuqian.com/img/20210727195039.jpg"> <br></p>
<div style="color:orange; border-bottom: 1px solid #d9d9d9;
    display: inline-block;
    color: #999;
    padding: 2px;">
图2.8 W0 sweep
</div>
</center></li>
<li><p>AC</p>
<ul>
<li><p>Frequency-Gain</p>
<center>
<p><img style="zoom:100%; border-radius: 0.3125em; margin: auto;" src="https://pic.zhouyuqian.com/img/20210727195100.jpg"> <br></p>
<div style="color:orange; border-bottom: 1px solid #d9d9d9;
    display: inline-block;
    color: #999;
    padding: 2px;">
图2.9 频率-增益曲线
</div>
</center></li>
<li><p>Frequency-Phase</p>
<center>
<p><img style="zoom:100%; border-radius: 0.3125em; margin: auto;" src="https://pic.zhouyuqian.com/img/20210727195114.jpg"> <br></p>
<div style="color:orange; border-bottom: 1px solid #d9d9d9;
    display: inline-block;
    color: #999;
    padding: 2px;">
图2.10 频率-相位曲线
</div>
</center></li>
</ul></li>
</ul>
<h1 id="共栅极">3. 共栅极</h1>
<blockquote>
<p>TODO</p>
</blockquote>
<h1 id="共源共栅">4. 共源共栅</h1>
<blockquote>
<p>TODO</p>
</blockquote>

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